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Physics book like spivak's calculus

  1. Apr 20, 2012 #1
    Hello,
    I am studying electromagnetism and I can't skip a topic and go to the next unless I learn it. Can any one please suggest a physics book and a calculus book on multivariables as rigorous as spivak's calculus?
    thanks
     
    Last edited: Apr 20, 2012
  2. jcsd
  3. Apr 20, 2012 #2
  4. Apr 20, 2012 #3
    I'm not familiar with this text but it covers very advanced topics. I kind of doubt that is a good book for someone who also asked for a book on multivariable calc.

    To the OP, I don't have experience with this book but you may want to read about https://www.amazon.com/Electricity-Magnetism-Berkeley-Physics-Course/dp/0070049084/ref=pd_sim_b_30 more.
     
  5. Apr 20, 2012 #4
  6. Apr 20, 2012 #5
    I see what you mean, I tend to like formal rigour so Schwinger's text seems right up my alley. I wouldn't have even looked at it unless I had my courses in complex variables, PDE's and fourier analysis though and even skimming the book seems very daunting. For a junior senior undergrad without as much math probably wangsness is a better text.

    https://www.amazon.com/Electromagnetic-Fields-Roald-K-Wangsness/dp/0471811866
     
  7. Apr 20, 2012 #6

    micromass

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    For multivariable, I can recommend Fleming's "Functions in several variables". Quite rigorous and complete book, but also elementary. It goes right up to proving Stokes theorem.
     
  8. Apr 26, 2012 #7
    Spivak's 'Calculus on Manifolds' is a multivariable calculus book similar in rigor to Spivak's 'Calculus', as is Munkre's 'Analysis on Manifolds'. You should be able to handle the first 3 chapters of Calc on Manifolds with little issue (no issue if you have some linear algebra under your belt). Chapters 4 and 5 are much more difficult IMO.

    You can try going right into them, but if it turns out to be too much Bachman's 'A Geometric Approach to Differential Forms' is a more elementary (but less rigorous) guide to the subject matter of these chapters. You could read this to get a feel for the material, and then go back to Calculus on Manifolds. If I recall correctly, both books are around 130 pages. Bachman's book mostly has problems with calculations as opposed to proofs, which would also be useful.
     
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